A priori mesh quality metric error analysis applied to a high-order finite element method

DOI10.1016/j.jcp.2011.03.036zbMath1220.65125OpenAlexW1981449925MaRDI QIDQ550975

Yong-Cai Geng, Sumit K. Garg

Publication date: 13 July 2011

Published in: Journal of Computational Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jcp.2011.03.036

zbMATH Keywords

convergencenumerical examplesfinite elementmagnetohydrodynamicsadvection equationspectral elementmesh deformationmesh quality metrics

Mathematics Subject Classification ID

Finite element methods applied to problems in fluid mechanics (76M10) Magnetohydrodynamics and electrohydrodynamics (76W05) Finite element, Rayleigh-Ritz and Galerkin methods for initial value and initial-boundary value problems involving PDEs (65M60) Error bounds for initial value and initial-boundary value problems involving PDEs (65M15) Mesh generation, refinement, and adaptive methods for the numerical solution of initial value and initial-boundary value problems involving PDEs (65M50) Initial value problems for first-order hyperbolic systems (35L45)

Related Items

Adaptive Quadrature and Remeshing Strategies for the Finite Cell Method at Large Deformations, A priori mesh quality metrics for three-dimensional hybrid grids, Non-iterative generation of an optimal mesh for a blade passage using deep reinforcement learning, The Target-Matrix Optimization Paradigm for High-Order Meshes, A remeshing strategy for large deformations in the finite cell method

Uses Software

• SLEPc
• SEL/HiFi

Cites Work

• The SEL macroscopic modeling code
• A priori mesh quality estimation via direct relation between truncation error and mesh distortion
• Mesh quality: A function of geometry, error estimates or both?
• Algebraic mesh quality metrics for unstructured initial meshes.
• Algebraic Mesh Quality Metrics
• A priori error estimates for numerical methods for scalar conservation laws. Part II : flux-splitting monotone schemes on irregular Cartesian grids
• SLEPc
• A nodal spectral stiffness matrix for the finite-element method
• On the Angle Condition in the Finite Element Method
• Tetrahedral mesh improvement via optimization of the element condition number